This better answers the question as it explains how to do it from the command line with ffmpeg, as specified in the original question. I think this answer should be marked as correct. As of May 2017 on Fedora 25, this still works, albeit a deprecation message for the MP4 codec.
– Justin W. FloryMay 26 '17 at 6:16

I solved a similar problem — I had a .MOV that was taken upside-down (i.e., rotated 180 degrees) which I wanted to set right.

On my Ubuntu 14.04 system, I ran avconv with essentially the same command-line options as given for ffmpeg in evilsoup's answer. Apparently, it does not support a transpose option for 180-degree rotation, so I did the 90-degree clockwise (i.e., transpose=1) twice.

When I tried minimal options, I got a message to the effect that:

encoder 'aac' is experimental and might produce bad results.
Add '-strict experimental' if you want to use it.

and the output file was zero length, so I added the -strict experimental.

Welcome to Super User. (1) While some background information in your answer may be helpful, it’s best to focus on your solution to the problem. I’ve edited your answer to illustrate; feel free to edit it further if you believe that I changed too much. (2) The display order of answers may vary; it’s better to identify other answer(s) explicitly rather than saying “above”. (2½) I hope you presented your avconv command lines in their entirety, and not just the differences from the ffmpeg command. Your answer should be self-sufficient; the other answer might go away. (3) Good luck!
– G-ManJun 8 '15 at 4:25

Also, I assume that when you say “result was satisfactory” you mean that your “result” file looked as good as the original file. You might want to (edit your message to) say so explicitly. (Such information — i.e., whether you lost video quality visible to the eye — is important to your answer, and shouldn’t be hidden away in a comment.) Also, I betcha you could leave out the quotes and say just -filter:v transpose=1 ….
– G-ManJun 8 '15 at 4:26